Shocks and cold fronts in merging and massive galaxy clusters: new detections with Chandra

2018

Publication Year

2020-11-12T10:41:27Z

Acceptance in OA@INAF

Shocks and cold fronts in merging and massive galaxy clusters: new detections

with Chandra

Title

Botteon, A.; GASTALDELLO, FABIO; BRUNETTI, GIANFRANCO

Authors

10.1093/mnras/sty598

DOI

http://hdl.handle.net/20.500.12386/28274

Handle

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY

Journal

476

Number

2020-11-12T10:41:27Z

Acceptance in OA@INAF

Shocks and cold fronts in merging and massive galaxy clusters: new detections

with Chandra

Title

Botteon, A.; GASTALDELLO, FABIO; BRUNETTI, GIANFRANCO

Authors

10.1093/mnras/sty598

DOI

http://hdl.handle.net/20.500.12386/28274

Handle

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY

Journal

476

Number

MNRAS 476, 5591–5620 (2018) doi:10.1093/mnras/sty598

Advance Access publication 2018 March 7

Shocks and cold fronts in merging and massive galaxy clusters: new

detections with Chandra

A. Botteon,

F. Gastaldello

and G. Brunetti

1_{Dipartimento di Fisica e Astronomia, Universit`a di Bologna, via P. Gobetti 93/2, I-40129 Bologna, Italy} 2_{INAF – IRA, via P. Gobetti 101, I-40129 Bologna, Italy}

3_{INAF – IASF Milano, via E. Bassini 15, I-20133 Milano, Italy}

Accepted 2018 March 1. Received 2018 February 22; in original form 2017 July 22

A B S T R A C T

A number of merging galaxy clusters show the presence of shocks and cold fronts, i.e. sharp discontinuities in surface brightness and temperature. The observation of these features requires an X-ray telescope with high spatial resolution like Chandra, and allows to study important aspects concerning the physics of the intracluster medium (ICM), such as its thermal conduction and viscosity, as well as to provide information on the physical conditions leading to the acceleration of cosmic rays and magnetic field amplification in the cluster environment. In this work we search for new discontinuities in 15 merging and massive clusters observed with Chandra by using different imaging and spectral techniques of X-ray observations. Our analysis led to the discovery of 22 edges: six shocks, eight cold fronts, and eight with uncertain origin. All the six shocks detected haveM < 2 derived from density and temperature jumps. This work contributed to increase the number of discontinuities detected in clusters and shows the potential of combining diverse approaches aimed to identify edges in the ICM. A radio follow-up of the shocks discovered in this paper will be useful to study the connection between weak shocks and radio relics.

Key words: shock waves – galaxies: clusters: general – galaxies: clusters: intracluster medium – X-rays: galaxies: clusters.

1 I N T R O D U C T I O N

Galaxy clusters are the most massive collapsed objects in the Universe. Their total mass is dominated by the dark matter (∼80 per cent) that shapes deep potential wells where the baryons (∼20 per cent) virialize. The majority of the baryonic matter in clusters is in the form of intracluster medium (ICM), a hot (kT∼ 2– 10 keV) and tenuous (n∼ 10−3–10−4cm−3) plasma emitting via thermal bremsstrahlung in the X-rays. In the past two decades,

Chandra and XMM–Newton established a dichotomy between

cool-core (CC) and non-cool-cool-core (NCC) clusters (e.g. Molendi & Pizzo-lato2001), depending whether their core region shows a drop in the temperature profile or not. The reason of this drop is a natural conse-quence of the strongly peaked X-ray emissivity of relaxed systems that leads to the gas cooling in this denser environment, counterbal-anced by the active galactic nucleus (AGN) feedback (e.g. Peterson & Fabian2006, for a review). On the other hand, disturbed systems exhibit shallower X-ray emissivity, hence lower cooling rates. For this reason there is a connection between the properties of the clus-ter core to its dynamical state: relaxed (i.e. in equilibrium) systems

_{E-mail:[email protected]}

naturally end to form a CC, while NCCs are typically found in un-relaxed objects (e.g. Leccardi, Rossetti & Molendi2010), where the effects of energetic events such as mergers have tremendous impact on their core, leading either to its direct disruption (e.g. Russell et al.

2012; Rossetti et al.2013; Wang, Markevitch & Giacintucci2016) or to its mixing with the surrounding hot gas (ZuHone, Markevitch & Johnson2010).

In the hierarchical process of large-scale structures formation the cluster mass is assembled from aggregation and infall of smaller structures (e.g. Kravtsov & Borgani2012, for a review). Mergers between galaxy clusters are the most energetic phenomena in the Universe, with the total kinetic energy that is dissipated in a cross-ing time-scale (∼Gyr) during the collision in the range 1063–64_erg.

At this stage shock waves, cold fronts, hydrodynamic instabilities, turbulence, and non-thermal components are generated in the ICM, making merging clusters unique probes to study several aspects of plasma astrophysics.

The subarcsec resolution of Chandra in particular allowed de-tailed studies of previously unseen edges, i.e. shocks and cold fronts (see Markevitch & Vikhlinin2007, for a review). Both are sharp surface brightness (SB) discontinuities that differ in the sign of the temperature jump across the front. Shocks mark pressure disconti-nuities where the gas is heated in the downstream (i.e. post-shock)

region, showing higher temperature values with respect to the up-stream (i.e. pre-shock) region. In cold fronts, instead, this jump is inverted and the pressure across the edge is almost continuous.

Shocks and cold fronts have been observed in several galaxy clus-ters that are clearly undergoing significant merging activity (e.g. Markevitch & Vikhlinin2007; Owers et al.2009; Ghizzardi, Ros-setti & Molendi2010; Markevitch2010, for some collections). The most remarkable example is probably the Bullet Cluster (Marke-vitch et al.2002), where an infalling subcluster (the ‘Bullet’) creates a contact discontinuity between its dense and low-entropy core and the surrounding hot gas. Ahead of this cold front another drop in SB but with reversed temperature jump, i.e. a shock front, is also detected. The observation of this kind of fronts requires that the col-lision occurs almost in the plane of the sky as projection effects can hide the SB and temperature jumps. Since shocks move quickly in cluster outskirts, in regions where the thermal brightness is fainter, they are more difficult to observe than cold fronts.

To be thorough, we mention that also morphologically relaxed clusters can exhibit SB discontinuities. However, in this case their origin is different: shocks can be associated with the outbursts of the central AGN (e.g. Forman et al.2005; McNamara et al.2005; Nulsen et al. 2005) and cold fronts can be produced by sloshing motions of the cluster core that are likely induced by off-axis minor mergers (e.g. Ascasibar & Markevitch2006; Roediger et al.2011,

2012).

The observation of shocks and cold fronts allows to investigate relevant physical processes in the ICM. Shocks (and turbulence) are able to (re)-accelerate particles and amplify magnetic fields lead-ing to the formation of cluster-scale diffuse radio emission known as radio relics (and radio haloes; e.g. Brunetti & Jones2014, for a review). In the presence of a strong shock it is also possible to investigate the electron–ion equilibration time-scale in the ICM (Markevitch2006). Cold fronts are complementary probes of the ICM microphysics (see ZuHone & Roediger 2016, for a recent review). The absence of Rayleigh–Taylor or Kelvin–Helmholtz in-stabilities in these sharp discontinuities indeed gives information on the suppression of transport mechanisms in the ICM (e.g. Ettori & Fabian2000; Vikhlinin, Markevitch & Murray2001a,b; however, see Ichinohe et al.2017). The cold fronts generated by the infalling of groups and galaxies in clusters (e.g. Eckert et al.2014,2017; Ichinohe et al. 2015; De Grandi et al.2016; Su et al.2017, for recent works) enable the study of other physical processes, such as magnetic draping and ram pressure stripping, providing information on the plasma mixing in the ICM (e.g. Dursi & Pfrommer2008, and references therein).

Currently, the number of detected edges in galaxy clusters is modest for observational limitations. This is reflected in the hand-ful of merger shocks that have been confirmed using both X-ray imaging and spectral analysis. In this work we aim to search in an objective way for new merger-induced shocks and cold fronts in massive and NCC galaxy clusters. The reason is to look for elusive features that can be followed-up in the radio band. To do that in practice we analysed 15 clusters that were essentially se-lected because of the existence of adequate X-ray data available in the Chandra archive. The Chandra satellite is the best instru-ment capable to resolve these sharp edges thanks to its excel-lent spatial resolution. We applied different techniques for spatial and spectral analysis including the application of an edge detec-tion algorithm on the cluster images, the extracdetec-tion and fitting of SB profiles, the spectral modelling of the X-ray (astrophysi-cal and instrumental) background, and the production of maps of the ICM thermodynamical quantities. This analysis is designed to

properly characterize sharp edges distinguishing shocks from cold fronts.

The paper is organized as follows. In Section 2 we present the cluster sample. In Section 3 we outline the edge-detection proce-dure and provide details about the X-ray data reduction (see also Appendices A and B). In Section 4 we describe how shocks and cold fronts were characterized in the analysis, and in Section 5 we present our results. Finally, in Section 6 we summarize and discuss our work.

Throughout the paper, we assume a  cold dark matter (CDM) cosmology with = 0.7, m= 0.3, and H0= 70 km s−1Mpc−1.

Statistical errors are provided at the 1σ confidence level, unless stated otherwise.

2 C L U S T E R S A M P L E

We selected a number of galaxy clusters where it is likely to detect merger-induced discontinuities searching for (i) massive systems in a dynamical disturbed state and (ii) with an adequate X-ray count statistics, based on current observations available in the Chandra archive. In particular the following.

(i) Using the Planck Sunyaev–Zel’dovich (SZ) catalogue (PSZ1; Planck Collaboration XXIX2014) we selected clusters with mass,1

as inferred from the SZ signal, M500>5× 1014M. Searching

for diffuse radio emission connected with shocks (radio relics and edges of radio haloes) is a natural follow-up of our study, hence this high mass threshold has been set mainly because non-thermal emission is more easily detectable in massive merging systems (e.g. Cassano et al.2013; de Gasperin et al.2014; Cuciti et al.2015). As a second step, we select only dynamically active systems excluding all the CC clusters. To do that we used the Archive of Chandra Cluster Entropy Profile Tables (ACCEPT; Cavagnolo et al.2009) and the recent compilation by Giacintucci et al. (2017) to look for the so-called core entropy value K0(see equation 4 in Cavagnolo

et al.2009), which is a good proxy to identify NCC systems (e.g. McCarthy et al.2007): clusters with K0<30–50 keV cm2exhibit

all the properties of a CC hence they were excluded in our analysis. (ii) Detecting shocks and cold fronts requires adequate X-ray count statistics as in particular the latter discontinuities are found in cluster outskirts, where the X-ray brightness is faint. For this reason, among the systems found in the Chandra data archive2_satisfying

(i), we excluded clusters with4–5 × 104_{counts in the Chandra}

broad-band 0.5–7.0 keV with the exposure available at the time of writing. We did that by converting the ROSAT flux in the 0.1–2.4 keV band reported in the main X-ray galaxy cluster catalogues [Bright-est Cluster Sample (BCS), Ebeling et al.1998; extended Brightest Cluster Sample (eBCS), Ebeling et al.2000; Northern ROSAT All-Sky (NORAS), B¨ohringer et al.2000; ROSAT–ESO Flux Limited X-ray (REFLEX), B¨ohringer et al.2004; MAssive Cluster Survey (MACS), Ebeling et al.2007,2010] into a Chandra count rate us-ing thePIMMSsoftware3and assuming a thermal emission model.

Clusters without a reported ROSAT flux in the catalogues were in-dividually checked by measuring the counts in circle enclosing the cluster SB profile when it is below the level of the background and thus rejected adopting the same count threshold.

1_M

500is the mass within the radius that encloses a mean overdensity of 500 with respect to the critical density at the cluster redshift.

2_{http://cda.harvard.edu/chaser/}

Shocks and cold fronts in galaxy clusters

5593

Table 1. The galaxy clusters analysed in this work (top) and the ones that have been excluded as the presence of a shock/cold front (or both) has been already claimed (bottom). Reported values of M500and K0are taken from Planck Collaboration XXIX (2014) and Cavagnolo et al. (2009), respectively.

Cluster name RA (J2000) Dec. (J2000) M500 z K0 Shock Cold front

(h m s_{) (}◦ _{) (10}14_M

) (keV cm2_{) (ref.) (ref.)}

A2813 00 43 24 −20 37 17 9.16 0.292 268± 44 – – A370 02 39 50 −01 35 08 7.63 0.375 322± 91 ˜1 A399 02 57 56 +13 00 59 5.29 0.072 153± 19 – 1 A401 02 58 57 +13 34 46 6.84 0.074 167± 8 – 1 MACS J0417.5−1154 04 17 35 −11 54 34 11.7 0.440 27± 7 – 1 RXC J0528.9−3927 05 28 53 −39 28 18 7.31 0.284 73± 14 – 1 MACS J0553.4−3342 05 53 27 −33 42 53 9.39 0.407 – 1 1 AS592 06 38 46 −53 58 45 6.71 0.222 59± 14 1 _– A1413 11 55 19 +23 24 31 5.98 0.143 164± 8 – – A1689 13 11 29 −01 20 17 8.86 0.183 78± 8 – – A1914 14 26 02 +37 49 38 6.97 0.171 107± 18 1 1 A2104 15 40 07 −03 18 29 5.91 0.153 161± 42 1 _– A2218 16 35 52 +66 12 52 6.41 0.176 289± 20 1 _– Triangulum Australis 16 38 20 −64 30 59 7.91 0.051 – ˜1 A3827 22 01 56 −59 56 58 5.93 0.098 165± 12 – – A2744 00 14 19 −30 23 22 9.56 0.308 438± 59 2 3 A115 00 55 60 +26 22 41 7.20 0.197 – 4 – El Gordo 01 02 53 −49 15 19 8.80 0.870 – 5 _– 3C 438 01 55 52 +38 00 30 7.35 0.290 – 6 6 A520 04 54 19 +02 56 49 7.06 0.199 325± 29 7 – A521 04 54 09 −10 14 19 6.90 0.253 260± 36 8 8 Toothbrush Cluster 06 03 13 +42 12 31 11.1 0.225 – 9, 10 10 Bullet Cluster 06 58 31 −55 56 49 12.4 0.296 307± 19 11, 12 11 MACS J0717.5+3745 07 17 31 +37 45 30 11.2 0.546 220± 96 – 13 A665 08 30 45 +65 52 55 8.23 0.182 135± 23 14 14 A3411 08 41 55 −17 29 05 6.48 0.169 270± 5 15 _– A754 09 09 08 −09 39 58 6.68 0.054 270± 24 16 17 MACS J1149.5+2223 11 49 35 +22 24 11 8.55 0.544 281± 39 – 18 Coma Cluster 12 59 49 +27 58 50 5.29 0.023 – 19, 20 _– A1758 13 32 32 +50 30 37 7.99 0.279 231± 37 – 21 A2142 15 58 21 +27 13 37 8.81 0.091 68± 3 – 22 A2219 16 40 21 +46 42 21 11.0 0.226 412± 43 23 _– A2256 17 03 43 +78 43 03 6.34 0.058 350± 12 24 25 A2255 17 12 31 +64 05 33 5.18 0.081 529± 28 26 _– A2319 19 21 09 +43 57 30 8.59 0.056 270± 5 – 27 A3667 20 12 30 −56 49 55 5.77 0.056 160± 15 28, 29 30 AC114 22 58 52 −34 46 55 7.78 0.312 200± 28 – 31

Notes. References:1_{this work (if a tilde is superimposed the edge nature is uncertain);}2_{Eckert et al. (2016);}3_{Owers et al. (2011);}4_{Botteon et al. (2016a);} 5_{Botteon et al. (2016b);}6_{Emery et al. (2017);}7_{Markevitch et al. (2005);}8_{Bourdin et al. (2013);}9_{Ogrean et al. (2013);}10_{van Weeren et al. (2016);}11_Markevitch et al. (2002);12_{Shimwell et al. (2015);}13_{van Weeren et al. (2017b);}14_{Dasadia et al. (2016);}15_{van Weeren et al. (2017a);}16_{Macario et al. (2011);}17_Ghizzardi et al. (2010);18_{Ogrean et al. (2016);}19_{Akamatsu et al. (2013);}20_{Ogrean & Br¨uggen (2013);}21_{David & Kempner (2004);}22_{Markevitch et al. (2000);}23_Canning et al. (2017);24_{Trasatti et al. (2015);}25_{Sun et al. (2002);}26_{Akamatsu et al. (2017a);}27_{O’Hara, Mohr & Guerrero (2004);}28_{Finoguenov et al. (2010);}29_Storm et al. (2017);30_{Vikhlinin et al. (2001b);}31_{De Filippis et al. (2004).}

We ended up with 37 massive and NCC cluster candidates for our study (Table1). In 22 of these systems (bottom of Table1) shocks/cold fronts (or both) have been already discovered and con-sequently we focused on the analysis of the remaining 15 clusters (top of Table1). We anticipate that the results on the detection of shocks and cold fronts in these clusters are summarized in Sec-tion 5.2.

3 M E T H O D S A N D DATA A N A LY S I S

To firmly claim the presence of a shock or a cold front in the ICM, both imaging and spectral analysis are required. Our aim is to search for SB and temperature discontinuities in the most objective way as possible, without being too much biased by prior constraints due

to guesses of the merger geometry or presence of features at other wavelengths (e.g. a radio relic). To do so we did the following.

(i) Applied an edge detection filter to pinpoint possible edges in the clusters that were also searched visually in the X-ray images for a comparison.

(ii) Selected the most clear features three times above the root mean square noise level of the filtered images following a coherent arc-shaped structure extending for >100 kpc in length.

(iii) Investigated deeper the pre-selected edges with the extrac-tion and fitting of SB profiles.

(iv) Performed the spectral analysis in dedicated spectral regions to confirm the nature of the jumps.

Table 2. Summary of the Chandra observations analysed in this work. The net exposure time is after the flare filtering. The averaged values of NH I(Kalberla et al.2005) and NH, tot(Willingale et al.2013) measured in the direction of the clusters are also reported; these are compared in Fig.1.

Cluster name Observation Detector Exposure Total exposure NH I NH, tot

ID (ACIS) (ks) (net ks) 1020_cm−2 ₁₀20_cm−2 9409, 16278, 16366 I, I, S 20, 8, 37 114 1.83 1.93 A2813  16491, 16513 S, S 37, 30 A370 515†, 7715 S∗, I 90, 7 64 3.01 3.32 A399 3230 I 50 42 10.6 17.1 518†, 2309, 10416, 10417 I∗, I∗, I, I 18, 12, 5, 5 176 9.88 15.2 A401  10418, 10419, 14024 I, I, I 5, 5, 140 MACS J0417.5−1154 3270, 11759, 12010 I, I, I 12, 54, 26 87 3.31 3.87 RXC J0528.9−3927 4994, 15177, 15658 I, I, I 25, 17, 73 96 2.12 2.26 MACS J0553.4−3342 5813, 12244 I, I 10, 75 77 3.32 3.79 9420, 15176 I, I 20, 20 98 6.07 8.30 AS592  16572, 16598 I, I 46, 24 537, 1661, 5002 I, I, I 10, 10, 40 128 1.84 1.97 A1413  5003, 7696 I, I 75, 5 540, 1663, 5004 I∗, I∗, I 10, 10, 20 185 1.83 1.98 A1689  6930, 7289, 7701 I, I, I 80, 80, 5 A1914 542†, 3593 I, I 10, 20 23 1.06 1.10 A2104 895 S∗ 50 48 8.37 14.5 553†, 1454† I∗, I∗ 7, 13 47 2.60 2.83 A2218  1666, 7698 I, I 50, 5 Triangulum Australis 17481 I 50 49 11.5 17.0 A3827 3290 S 50 45 2.65 2.96

Notes. ObsIDs marked with†were excluded in the spectral analysis as the focal plane temperature was warmer than the standard−119.7◦C observations and there is not Charge Transfer Inefficiency correction available to apply to this data with subsequent uncertainties in the spectral analysis of these data sets. All the observations were taken in VFAINT mode except the ones marked by∗that were instead taken in FAINT mode.

In addition, we produced maps of the ICM thermodynamical quantities to help in the interpretation of the features found with the above-mentioned procedure.

In the following sections we describe into details the X-ray data analysis performed in this work.

3.1 X-ray data preparation

In Table2we report all the Chandra Advanced CCD Imaging Spec-trometer I-array (ACIS-I) and Advanced CCD Imaging Spectrome-ter S-array (ACIS-S) observations of our clusSpectrome-ter sample. Data were reprocessed withCIAOv4.9 and ChandraCALDBv4.7.3 starting from

level=1 event file. Observation periods affected by soft proton flares were excluded using the deflare task after the inspection of the light curves extracted in the 0.5–7.0 keV band. For ACIS-I, these where extracted from the front-illuminated S2 chip that was kept on during the observation or in one front-illuminated ACIS-I chip, avoiding the cluster diffuse emission, if S2 was turned off. In ACIS-S observations the target is imaged in the back-illuminated S3 chip hence light curves were extracted in S1, also back-illuminated.4

Cluster images were created in the 0.5–2.0 keV band and com-bined with the corresponding monochromatic exposure maps (given the restricted energy range) in order to produce exposure-corrected images binned to have a pixel size of 0.984 arcsec. The data sets of clusters observed multiple times (11 out of 15) were merged with merge_obsbefore this step.

The mkpsfmap script was used to create and match point spread function (PSF) map at 1.5 keV with the corresponding exposure

4_{In the ACIS-S ObsID 515 the light curve was extracted in S2 as S1 was} turned off.

map for every ObsID. For cluster with multiple ObsIDs we created a single exposure-corrected PSF map with minimum size. Thus, point sources were detected with the wavdetect task, confirmed by eye and excised in the further analysis.

3.2 Edge detection filter

In practice, the visual inspection of X-ray images allows to iden-tify the candidate discontinuities (Markevitch & Vikhlinin2007). We complement this approach with the visual inspection of fil-tered images. Sanders et al. (2016b) presented a Gaussian gradient magnitude (GGM) filter that aims to highlight the SB gradients in an image, similarly to the Sobel filter (but assuming Gaussian derivatives); in fact, it has been shown that these GGM images are particularly useful to identify candidate sharp edges, such as shocks and cold fronts (e.g. Walker, Sanders & Fabian2016). The choice of the Gaussian width σ in which the gradient is computed depends on the physical scale of interest, magnitude of the jump, and data qual-ity: edges become more visible with increasing jump size and count rate; this requires images filtered on multiple scales to best identify candidate discontinuities (e.g. Sanders et al.2016a,b). In this re-spect, we applied the GGM filter adopting σ= 1, 2, 4, and 8 pixels (a pixel corresponds to 0.984 arcsec) to the exposure-corrected im-ages of the clusters in our sample. We noticed that the use of small length filters (1 and 2 pixels) is generally ineffective in detecting discontinuities in cluster outskirts due to the low counts in these peripheral regions (see also Sanders et al.2016b). Instead Gaussian widths of σ= 4 and 8 pixels better highlight the SB gradients with-out saturating too much the ICM emission (as it would result with the application of filters with scales σ= 16 and 32 pixels). For this reason, here we will report GGM filtered images with these two scales.

Shocks and cold fronts in galaxy clusters

5595

3.3 Surface brightness profiles

After looking at X-ray and GGM images, we extracted and fit-ted SB profiles of the candidate discontinuities on the 0.5–2.0 keV exposure-corrected images of the clusters usingPROFFITv1.4

(Eck-ert, Molendi & Paltani2011). A background image was produced by matching (with reproject_event) the background templates to the corresponding event files for every ObsID. This was normal-ized by counts in the 9.5–12.0 keV band and subtracted in the SB analysis. Corrections were typically within 10 per cent except for the S3 chip in FAINT mode (ObsIDs 515 and 895) where the cor-rection was∼45 per cent. For clusters observed multiple times, all the ObsIDs were used in the fits. In the profiles, data were grouped to reach a minimum signal-to-noise ratio threshold per bin of 7.

3.4 Spectra

The scientific scope of our work requires a careful treatment of the background of X-ray spectra, as in particular shock fronts are typi-cally observed in the cluster outskirts, where the source counts are low. We modelled the background by extracting spectra in source-free regions at the edge of the field-of-view. This was not possible for ACIS-I observations of nearby objects and for clusters observed with ACIS-S as the ICM emission covers all the chip area. In this respect we used observations within 3◦to the target pointing (i.e. ObsID 15068 for A399 and A401, ObsID 3142 for A2104, ObsID 2365 for Triangulum Australis and ObsID 17881 for A3827) to model the components due to the cosmic X-ray background (CXB) and to the Galactic local foreground. The former is due to the super-position of the unresolved emission from distant point sources and can be modelled as a power law with photon index cxb= 1.42 (e.g.

Lumb et al.2002). The latter can be decomposed in two-temperature thermal emission components (Kuntz & Snowden2000) due to the Galactic Halo (GH) emission and the Local Hot Bubble (LHB), with temperature kTgh= 0.25 keV and kTlhb= 0.14 keV and solar

metallicity. Galactic absorption for GH and CXB was taken into account using the averaged values measured in the direction of the clusters from the Leiden/Argentine/Bonn (LAB) Survey of Galactic HI(Kalberla et al.2005). However, it has to be noticed that the total hydrogen column density is formally NH,tot= NHI+ 2NH2, where

NH2accounts for molecular hydrogen whose contribution seems to

be neglected for low-density columns. In Table2we reported the values of NHI(Kalberla et al.2005) and NH, tot(Willingale et al.

2013) in the direction of the clusters in our sample, while in Fig.1

we compared them. In Appendix A we discuss the five clusters (A399, A401, AS592, A2104, and Triangulum Australis) that do not lay on the linear correlation of Fig.1.

Additionally to the astrophysical CXB, GH, and LHB emission, an instrumental non-X-ray background (NXB) component due to the interaction of high-energy particles with the satellite and its electronics was considered. Overall, the background model we used can be summarized as

apec_lhb+ phabs ∗ (apec_gh+ powerlaw_cxb)+ bkg_nxb, (1) where theBKGnxbwas modelled with

expdec+ power +gaussian for ACIS-I,

expdec+ bknpower +gaussianfor ACIS-S,

(2)

where a number of Gaussian fluorescence emission lines were super-imposed on to the continua. For more details on the NXB modelling the reader is referred to Appendix B.

Figure 1. Comparison between the HIdensity column from Kalberla et al. (2005) and the total (HI+ H2) density column from Willingale et al. (2013). The dashed line indicates the linear correlation as a reference.

The ICM emission was described with a thermal model taking into account the Galactic absorption in the direction of the clusters (cf. Table2and Appendix A):

phabs∗ apecicm, (3)

the metallicity of the ICM was set to 0.3 Z_{ (e.g. Werner et al.}

2013).

Spectra were simultaneously fitted (using all the ObsIDs available for each cluster, unless stated otherwise) in the 0.5–11.0 keV energy band for ACIS-I and in the 0.7–10.0 keV band for ACIS-S, using the packageXSPECv12.9.0o with Anders & Grevesse (1989) abundances

table. Since the counts in cluster outskirts are poor, Cash statistics (Cash1979) was adopted.

3.4.1 Contour binning maps

We usedCONTBINv1.4 (Sanders2006) to produce projected maps of temperature, pressure, and entropy for all the clusters of our sample. The clusters were divided in regions varying the geometric constraint value (see Sanders2006, for details) according to the morphology of each individual object to better follow the SB con-tour of the ICM. We required∼2500 background-subtracted counts per bin in the 0.5–2.0 keV band. Spectra were extracted and fitted as described in the previous section.

While the temperature is a direct result of the spectral fitting, pressure and entropy require the passage through the normalization value of the thermal model, i.e.

N = 10−14

4π[DA(1+ z)]2



nenHdV (cm−5), (4)

where DAis the angular size distance to the source (cm), whereas ne

and nHare the electron and hydrogen density (cm−3), respectively.

The projected emission measure is

with A the area of each bin, and it is proportional to the square of the electron density integrated along the line of sight. Using equation (5) we can compute the pseudo-pressure,

P = kT (EM)1/2 _{(keV cm}−5/2_arcsec−1_{), (6)}

and pseudo-entropy,

K= kT (EM)−1/3 (keV cm5/3_arcsec−2/3_{), (7)}

values for each spectral bin. The prefix pseudo- underlines that these quantities are projected along the line of sight (e.g. Mazzotta et al.

2004).

4 C H A R AC T E R I Z AT I O N O F T H E E D G E S

The inspection of the cluster X-ray and GGM filtered images pro-vide the first indication of putative discontinuities in the ICM. These need to be characterized with standard imaging and spectral analysis techniques to be firmly claimed as edges.

The SB profiles of the candidate shocks and cold fronts were modelled assuming that the underlying density profile follows a broken power law (e.g. Markevitch & Vikhlinin2007, and refer-ences therein). In the case of spherical symmetry, the downstream and upstream (subscripts ‘d’ and ‘u’) densities differ by a factor

C ≡ nd/nuat the distance of the jump rj: nd(r)= Cn0  r rj a1 if r≤ rj, nu(r)= n0  r rj a2 if r > rj, (8)

where a1and a2are the power-law indices, n0is a normalization

factor, and r denotes the radius from the centre of the sector. In the fitting procedure all these quantities were free to vary. We stress that the values ofC reported throughout the paper have been deprojected along the line of sight under the spherical assumption byPROFFIT

(Eckert et al.2011).

A careful choice of the sector where the SB profile is extracted is needed to properly describe a sharp edge due to a shock or a cold front. In this respect, the GGM filtered images give a good start-ing point to delineate that region. Durstart-ing the analysis, we adopted different apertures, radial ranges, and positions for the extracting sectors, then we used the ones that maximize the jump with the best-fitting statistics. Errors reported forC however do not account for the systematics due to the sector choice.

Spectral fitting is necessary to discriminate the nature of a dis-continuity as the temperature ratioR ≡ Td/Tuis >1 in the case of

a shock and <1 in the case of a cold front (e.g. Markevitch et al.

2002). The temperature map can already provide indication about the sign of the jump. However, once that the edge position is well identified by the SB profile analysis, we can use a sector with the same aperture and centre of that maximizing the SB jump to extract spectra in dedicated sectors covering the downstream and upstream regions. In this way we can carry out a self-consistent analysis and avoid possible contamination due to large spectral bins that might contain plasma at different temperature unrelated to the shock/cold front.

In the case of a shock, the Mach numberM can be determined by using the Rankine–Hugoniot jump conditions (e.g. Landau & Lifshitz1959) for the density,

C ≡ nd nu= 4M2 SB M2 SB+ 3 , (9) and temperature, R ≡Td Tu = 5M4kT+ 14M 2 kT− 3 16M2 kT , (10)

here reported for the case of monatomic gas.

5 R E S U LT S

We find 29 arc-shaped features three times above the root mean square noise level in the GGM filtered images, 22 of them were found to trace edges in the SB profiles. In Figs2–12 and14–17

we show a Chandra image in the 0.5–2.0 keV energy band, the products of the GGM filters, the maps of the ICM thermodynamical quantities, and the SB profiles for each cluster of the sample. The C-stat/dof and the temperature fractional error for each spectral region are reported in Appendix C. The edges are highlighted in the Chandra images in white for shocks and in green for cold fronts. Discontinuities for whose spectral analysis does not firmly allow this distinction are reported in yellow. The temperature values obtained by fitting spectra in dedicated upstream and downstream regions are reported in shaded boxes (whose lengths cover the radial extent of the spectral region) in the panels showing the SB profiles. If the jump was detected also in temperature, the box is coloured in red for the hot gas and in blue for the cold gas; conversely, if the upstream and downstream temperatures are consistent (within 1σ ), the box is displayed in yellow. As a general approach, in the case of weak discontinuities we also compare results with the best fit obtained with a single power-law model.

In the following we discuss the individual cases. In particular, in Sections 5.1 and 5.3 we report the clusters with and without detected edges, respectively. The results of our detections are summarized in Section 5.2 and in Table3. In Appendix D we show the seven arc-like features selected by the GGM filtered images that do not present a discontinuity in the SB profile fitting.

5.1 Detections 5.1.1 A370

This represents the most distant object in Abell catalogue (Abell, Corwin & Olowin1989), at a redshift of z= 0.375. It is famous to be one of the first galaxy clusters where a gravitational lens was observed (Soucail et al.1987; Kneib et al.1993). The X-ray emission is elongated in the north (N)-south (S) direction (Fig.2a); the bright source to the N is a nearby (z= 0.044) elliptical galaxy not associated with the cluster.

A370 was observed two times with Chandra. The longer obser-vation (ObsID 515) was performed in an early epoch after Chandra launch in which an accurate modelling of the ACIS background is not possible, making the spectral analysis of this data set unfeasible (see notes in Table2for more details). The other observation of A370 (ObsID 7715) is instead very short. For this reason we did only a spatial analysis for this target.

The GGM images in Figs2(b) and (c) suggest the presence of a rapid SB variation both in the west (W) and east (E) direction. The SB profiles taken across these directions were precisely modelled in our fits in Figs2(d) and (e), revealing jumps with similar entity (C ∼ 1.5). The inability of performing spectral analysis in this cluster leaves their origin unknown. An additional SB gradient sug-gested by the GGM images towards the S direction did not reveal the presence of an edge with the SB profile fitting (Fig.D1).

Shocks and cold fronts in galaxy clusters

5597

Figure 2. A370. Chandra 0.5–2.0 keV image (a), GGM filtered images on scales of 4 (b) and 8 (c) pixels and best-fitting broken power-law (solid blue) and single power-law (dashed red) models (residuals on the bottom are referred to the former) of the extracted SB profiles (d and e). The sectors where the SB profiles were fitted and the positions of the relative edges are marked in the Chandra image in yellow.

5.1.2 A399 and A401

These two objects constitute a close system (z= 0.072 and 0.074, respectively) of two interacting galaxy clusters (e.g. Fujita et al.

1996). Their X-ray morphology is disturbed (Figs3a and4a) and the ICM temperature distribution irregular (Bourdin & Mazzotta

2008), revealing the unrelaxed state of the clusters. Recently, Aka-matsu et al. (2017b) claimed the presence of an accretion shock between the two using Suzaku data. This cluster pair hosts two ra-dio haloes (Murgia et al.2010). The boundary of the halo in A399 is coincident with an X-ray edge, as already suggested by XMM–

Newton observations (Sakelliou & Ponman2004).

Only one Chandra observation is available for A399, whereas several observations were performed on A401. Despite this, we only used ObsID 14024 (which constitutes the 74 per cent of the total observing time) to produce the maps shown in Figs4(d)–(f) as the remainder ObsIDs are snapshots that partially cover the cluster emission. This is also the only case where we required∼5000 counts

in each spectral bin given the combination of high brightness and long exposure on A401.

The temperature maps in Figs3(d) and4(d) indicate an overall hot ICM and the presence of some hot substructures, in agreement with previous studies (Sakelliou & Ponman2004; Bourdin & Mazzotta

2008).

The GGM images of A399 reveal a SB gradient towards the south-east (SE) direction. The SB profile across this region and its temperature jump reported in Fig.3(g) show that this ‘inner’ edge is a cold front with R = 0.74+0.14_−0.12 and C = 1.72+0.13_−0.12. Ahead of that, the X-ray SB rapidly fades away, as well as the radio emis-sion of the halo (Murgia et al.2010). The ‘outer’ SB profile in this direction indeed shows another discontinuity with C = 1.45+0.10_−0.10 (Fig.3h). The broken power-law model provides a better descrip-tion of the data (χ2_{/d.o.f.= 68.6/72) compared to a single}

power-law fit (χ2_{/d.o.f.= 122.6/74), corresponding to a null-hypothesis}

Figure 3. A399. Chandra 0.5–2.0 keV image (a), GGM filtered images on scales of 4 (b) and 8 (c) pixels, projected maps of temperature (d), pressure (e), entropy (f), and best-fitting broken power-law (solid blue) and single power-law (dashed red) models (residuals on the bottom are referred to the former) of the extracted SB profiles (g and h). The goodness of fits is reported in Fig.C1. The sectors where the SB profiles were fitted and the positions of the relative edges are marked in the Chandra image in green (cold front) and yellow. The dashed arcs show the radial limits used for measuring the temperature downstream and upstream the front, which values (in keV) are reported in the shaded boxes in the SB profiles. Note that in the GGM filtered images the straight and perpendicular features are artefacts due to chip gaps.

Shocks and cold fronts in galaxy clusters

5599

Figure 4. A401. The same as for Fig.3. The goodness of fits is reported in Fig.C2. The position of the edge is marked in the Chandra image in green (cold front).

however, the temperatures across the edge are consistent, not al-lowing us to firmly claim the nature of the SB jump. We mention that the presence of a shock would be in agreement with the fact that cold fronts sometimes follow shocks (e.g. Markevitch et al.

2002) and that shocks might (re)-accelerate cosmic rays producing

the synchrotron emission at the boundary of some radio haloes (e.g. Shimwell et al.2014).

A401 has a more elliptical X-ray morphology and an average temperature higher than A399. The hottest part of the ICM is found on the E direction. Indeed, the GGM image with σ = 8 pixels in

Fig.4(c) highlights a kind of spiral structure in SB on this side of the cluster, with maximum contrast towards the SE. The SB profile in this sector is well described by a broken power law with compres-sion factorC = 1.39+0.04_−0.04 (Fig.4g). The higher temperature in the upstream region (kTu= 10.4+0.8_−0.6keV against kTd= 8.1+0.4_−0.4keV)

confirms that this is a cold front. This could be part of a bigger spiral-shaped structure generated by a sloshing motion.

5.1.3 MACS J0417.5−1154

It is the most massive (M500= 1.2 × 1015M) and most distant

(z= 0.440) cluster of our sample. Its extremely elongated X-ray morphology (Fig.5a) suggests that this cluster is undergoing a high-speed merger (Ebeling et al.2010; Mann & Ebeling2012). Despite this, the value of K0= 27 ± 7 keV cm2indicates that its compact

core has not been disrupted yet, acting as a ‘bullet’ in the ICM (e.g. Markevitch et al.2002, for a similar case). Radio observations show the presence of a giant radio halo that remarkably follows the ICM thermal emission (Dwarakanath, Malu & Kale2011; Parekh et al.

2017).

The most striking feature of MACS J0417.5−1154 is certainly its prominent cold front in the SE generated by an infalling cold and low-entropy structure, as highlighted by our maps in Figs5(d)– (f). The SB across this region abruptly drops (C = 2.44+0.31_−0.25) in the upstream region (Fig.5g), for which spectral analysis provided a clear jump in temperature ofR = 0.44+0.17_−0.10, leading us to confirm the cold front nature of the discontinuity. The high-temperature value of kTu= 16.9+6.1_−3.3keV found upstream is an indication of a

shock-heated region; a shock is indeed expected in front of the CC similarly to other clusters observed in an analogous state (e.g. Markevitch et al.2002; Russell et al.2012; Botteon et al.2016b) and is also suggested by our temperature and pseudo-pressure maps. Nonetheless, we were not able to characterize the SB jump of this potential feature. On the opposite side, GGM images pinpoint an-other edge towards the north-west (NW) direction, representing again a huge jump (C = 2.50+0.29_−0.25) in the SB profile (Fig.5h). The spectral analysis in a dedicated region upstream of this feature al-lowed us only to set a lower limit of kTu>12.7 keV, suggesting the

presence of a hot plasma, in agreement with our temperature map and the one reported in Parekh et al. (2017), where the pressure is almost continuous (Fig.5e), as expected for a cold front.

5.1.4 RXC J0528.9−3927

No dedicated studies exist on this cluster located at z= 0.284. The ICM emission is peaked on the cluster core, the coldest region in the cluster (Finoguenov, B¨ohringer & Zhang2005), and fades in the outskirts where the emission is faint and diffuse (Fig.6a).

Our maps of the ICM thermodynamical quantities in Figs6(d)– (f) are rather affected by large spectral bins due to the low counts of the cluster. The X-ray emission is peaked on the central low-entropy region, which is surrounded by hot gas. An edge on the W is suggested both from the GGM images and from the above-mentioned maps. The SB profile in Fig.6(g) is well fitted with a broken power law with C = 1.51+0.10_−0.09 and the dedicated spectral analysis confirms the value reported in the temperature map (kTu=

10.5+3.6_−1.8keV and kTd= 7.2+0.9_−0.7keV), indicating the presence of a

cold front. Two more SB gradients pinpointed in the GGM images to the E and W directions did not provide evidence for any edge with the SB profile fitting (Fig.D2).

5.1.5 MACS J0553.4−3342

It is a distant cluster (z= 0.407) in a disturbed dynamical state, as shown from both optical and X-ray observations (Ebeling et al.

2010; Mann & Ebeling2012). The X-ray morphology (Fig.7a) suggests that a binary head-on merger is occurring approximately in the plane of the sky (Mann & Ebeling2012). No value of the central entropy K0 is reported in Cavagnolo et al. (2009) nor in

Giacintucci et al. (2017). A radio halo that follows the ICM emission has been detected in this system (Bonafede et al.2012). At the time of this writing, two more papers on MACS J0553.4−3342, both containing a joint analysis of Hubble Space Telescope and Chandra observations, were published (Ebeling, Qi & Richard2017; Pandge et al.2017).

The maps of the ICM thermodynamical quantities shown in Figs7(d)–(f) further support the scenario of an head-on merger in the E–W direction for MACS J0553.4−3342 in which a low-entropy structure is moving towards E, where GGM images highlight a steep SB gradient. This is confirmed by the SB profile fit (Fig.7g) that leads to a compression factor ofC = 2.49+0.32_−0.26, while the temper-ature jump found by spectral analysis ofR = 0.62+0.33_−0.18 indicates that this discontinuity is a cold front (see also Ebeling et al.2017; Pandge et al.2017). The high value of kTu= 13.7+6.9_−3.7keV suggests

a shock-heated region to the E of the cold front; indeed the ‘outer’ SB profile of Fig.7(h) indicates the presence of an edge in the clus-ter outskirts. We used for the characclus-terization of the SB profile a sector of aperture 133◦–193◦(where the angles are measured in an anticlockwise direction from W), whereas we used a wider sector (133◦–245◦) as depicted in Fig.7(a) to extract the spectra in order to ensure a better determination of the downstream and upstream tem-peratures, which ratio ofR = 2.00+1.14_−0.63confirms the presence of a shock with Mach numberMSB= 1.58+0.30_−0.22andMkT = 1.94+0.77_−0.56, respectively, derived from the SB and temperature jumps. This edge is spatially connected with the boundary of the radio halo found by Bonafede et al. (2012). On the opposite side of the cluster, another roundish SB gradient is suggested from the inspection of the GGM images (Figs7b and c). The W edge is well described by our fit (Fig.7i) that leads to C = 1.70+0.12_−0.11, while spectral analysis pro-videsR = 0.33+0.22_−0.12, consistent with the presence of another cold front. Even though the upstream temperature is poorly constrained, the spectral fit suggests high-temperature values, also noticed in Ebeling et al. (2017), possibly indicating another shock-heated re-gion ahead of this cold front; however, the presence of a possible discontinuity associated with this shock cannot be claimed with current data. The symmetry of the edges strongly supports the sce-nario of a head-on merger in the plane of the sky. However, the serious challenges to this simple interpretation described in Ebeling et al. (2017) in term of the relative positions of the brightest central galaxies, X-ray peaks, and dark matter distributions need to be re-considered in view of the presence and morphology of the extended X-ray tail discussed in Pandge et al. (2017) and clearly highlighted by the GGM image (see Fig.7c).

5.1.6 AS592

Known also with the alternative name RXC J0638.7−5358, this cluster located at z= 0.222 is one of those listed in the supplemen-tary table of southern objects of Abell et al. (1989). The ICM has an overall high temperature (Mantz et al.2010; Menanteau et al.

2010) and is clearly unrelaxed (Fig.8a), despite the fact that AS592 has one of the lowest K0value of our sample (cf. Table1).

Shocks and cold fronts in galaxy clusters

5601

Figure 5. MACS J0417. The same as for Fig.3. The goodness of fits is reported in Fig.C3. The positions of the edges are marked in the Chandra image in green (cold fronts).

Figure 6. RXC J0528. The same as for Fig.3. The goodness of fits is reported in Fig.C4. The position of the edge is marked in the Chandra image in green (cold front).

Shocks and cold fronts in galaxy clusters

5603

Figure 7. MACS J0553. The same as for Fig.3. The goodness of fits is reported in Fig.C5. The positions of the edges are marked in the Chandra image in green (cold fronts) and white (shock).

Figure 8. AS592. The same as for Fig.3. The goodness of fits is reported in Fig.C6. The position of the edge is marked in the Chandra image in white (shock).

Shocks and cold fronts in galaxy clusters

5605

The maps in Figs8(d)–(f) highlight the presence of two low-entropy and low-temperature CCs surrounded by an overall hot ICM. In the south-west (SW), a feature in SB is suggested from the GGM image with σ= 8 pixels. The analysis of the X-ray profile and spectra across it result in a SB discontinuity with compression factorC = 1.99+0.17_−0.15and temperature ratioR = 1.61+0.66_−0.43(Fig.8g), leading us to claim the presence of a shock front with Mach number derived from the SB jump ofMSB= 1.72+0.15_−0.12, in agreement with

that derived by the temperature jumpMkT = 1.61+0.54_−0.42. The SB variation indicated by the GGM images towards the north-east (NE) direction did not show the presence of a discontinuity with the SB profile fitting (Fig.D3).

5.1.7 A1914

It is a system at z= 0.171 in a complex merger state (e.g. Barrena, Girardi & Boschin2013), geometry of which is still not understood well (Mann & Ebeling2012). In particular, the irregular mass distri-bution inferred from weak lensing data (Okabe & Umetsu2008) is puzzling if compared to near-spherical X-ray emission of the ICM on larger scales (Fig.9a). Previous Chandra studies highlighted the presence of a heated ICM with temperature peak in the cluster centre (Govoni et al.2004; Baldi et al.2007). At low frequency, a bright steep spectrum source 4C 38.39 (Roland et al.1985) and a radio halo (Kempner & Sarazin2001) are detected.

Among the two Chandra observations on A1914 retrieved from the archive we had to discard ObsID 542 since it took place in an early epoch of the Chandra mission, as described above for the case of A370 (see also notes in Table2). We mention that in the Chandra archive other four data sets (ObsIDs 12197, 12892, 12893, and 12894) can be found for A1914. However, these are 5 ks snapshots pointed in four peripheral regions of the cluster that are not useful for our edge research; for this reason, they were excluded in our analysis.

Our maps of the ICM thermodynamical quantities in Figs9(d)– (f) indicate the presence of a bright low-entropy region close to the cluster centre with a lower temperature with respect to an over-all hot ICM. The adjacent spectral bin towards the E suggests the presence of high-temperature gas, while GGM images indicate a rapid SB variation. This feature is quite sharpened, recalling the shape of a tip, and cannot be described under a spherical assump-tion. For this reason two different, almost perpendicular, sectors were chosen to extract the SB profiles to the E, one in an ‘upper’ (towards the NE) and one a ‘lower’ (towards the SE) direction of the tip. Their fits in Figs9(g) and (h) both indicate a similar drop in SB (C ∼ 1.5). Spectra were instead fitted in joint regions down-stream and updown-stream of the two SB sectors, leading to a single value for kTuand kTd. The temperature jump is consistent with a cold

front (R = 0.40+0.21_−0.12). Although the large uncertainties, spectral analysis provides indication of a high upstream temperature, likely suggesting the presence of a shock-heated region. This scenario is similar to the Bullet Cluster (Markevitch et al.2002) and to the above-mentioned MACS J0417.5−1154. A shock moving into the outskirts cannot be claimed with the current data but it is already suggested in Figs9(g) and (h) by the hint of a slope change in the upstream power law in correspondence of the outer edge of the region that we used to extract the upstream spectrum. Another SB feature to the W direction is highlighted by the GGM images and confirmed by the profile shown in Fig.9(i). Its compression fac-tor ofC = 1.33+0.08_−0.07 and temperature ratio achieved from spectral analysis ofR = 1.27+0.26_−0.21allow us to claim the presence of a weak

shock with Mach number consistently derived from the SB and temperature jumps, i.e. MSB= 1.22+0.06_−0.05 and MkT = 1.28+0.26_−0.21, respectively. This underlines the striking similarly of A1914 with other head-on mergers where a countershock (i.e. a shock in the op-posite direction of the infalling subcluster) has been detected, such as the Bullet cluster (Shimwell et al.2015) and El Gordo (Botteon et al.2016b), for which it also shares a similar double tail X-ray morphology.

5.1.8 A2104

This is a rich cluster at z= 0.153. Few studies exist in the literature on A2104. Pierre et al. (1994) first revealed with ROSAT that this system is very luminous in the X-rays and has a hot ICM. This result was confirmed more recently with Chandra (Gu et al.2009), which also probed a slight elongation of the ICM in the NE–SW direction (Fig.10a) and a temperature profile declining towards the cluster centre (Baldi et al.2007).

The maps of the ICM thermodynamical quantities (Figs10d–f) and GGM filtered images (Figs10b and c) of A2104 confirm an overall high temperature of the system and some SB contrasts in the ICM. We extract SB profiles across two sectors towards the SE and one towards the SW directions. The most evident density jump (C = 1.54+0.16_−0.14) is detected for the SE ‘outer’ sector shown in Fig.10(h), while the others show only the hint of a discontinuity (Figs10g and i). However, the fit statistics of the broken power-law and single power-power-law models indicate that the jump model is in better agreement with the data in both the cases, being re-spectively χ2_{/d.o.f.= 17.2/16 and χ}2_{/d.o.f.= 37.4/18 for the}

SE ‘inner’ sector (3.1σ significance, F-test analysis), whereas it is χ2_{/d.o.f.= 64.5/63 and χ}2_{/d.o.f.= 122.5/65 for the SW}

sec-tor (6.0σ significance, F-test analysis). Spectral analysis allowed us only to find a clear temperature jump for the SE ‘inner’ edge, leaving the nature of the other two SB jumps more ambiguous. The temper-ature ratio across the SE ‘inner’ sector isR = 1.33+0.27_−0.19, leading us to claim a shock with Mach numberMkT = 1.34+0.26_−0.20, comparable to the one computed from the upper limit on the compression factor (C < 1.47) of the SB jump, i.e. MSB<1.32.

5.1.9 A2218

Located at z= 0.176, this cluster is one of the most spectacu-lar gravitational lens known (Kneib et al.1996). The system is in a dynamically unrelaxed state, as revealed by its irregular X-ray emission (Fig.11a; Machacek et al.2002) and by the substructures observed in optical (Girardi et al.1997). Detailed spectral analysis already provided indication of a hot ICM in the cluster centre (Gov-oni et al.2004; Pratt, B¨ohringer & Finoguenov2005; Baldi et al.

2007). A small and faint radio halo has also been detected in this system (Giovannini & Feretti2000).

Four Chandra observations exist on A2218. Unfortunately, two of these (ObsIDs 553 and 1454) cannot be used for the spectral analysis because, as mentioned above for A370 and A1914, they are early Chandra observations for which the ACIS background modelling is not possible (see notes in Table2for more details), hence we only used the remainder two ObsIDs to produce the maps shown in Fig.11.

The low counts on A2218 result in maps of the ICM thermo-dynamical quantities with large bins, as shown in Figs 11(d)– (f). The ICM temperature is peaked towards the cluster centre, in agreement with previous studies (Pratt et al.2005; Baldi et al.

Figure 9. A1914. The same as for Fig.3. The goodness of fits is reported in Fig.C7. The positions of the edges are marked in the Chandra image in green (cold front) and white (shock).

2007). The analysis of GGM images highlights the presence of rapid SB variations in more than one direction. The SB profile towards the N shows the greatest of these jumps, correspond-ing to C = 1.47+0.21_−0.18 (Fig. 11g). From the spectral analysis we achieve a temperature ratioR = 1.38+0.40_−0.28 across the edge, indi-cating the presence of a shock with consistent Mach number

de-rived from the SB jump, i.e.MSB= 1.32+0.15_−0.13, and from the

tem-perature jump, i.e.MkT = 1.39+0.37_−0.29. The presence of a shock in this cluster region is consistent with the temperature map varia-tions reported in Govoni et al. (2004). In the SE direction, there is indication of two discontinuities from the SB profile analysis (Figs11h and i): spectra suggest that the ‘inner’ discontinuity is

Shocks and cold fronts in galaxy clusters

5607

Figure 10. A2104. The same as for Fig.3. The goodness of fits is reported in Fig.C8. The positions of the edges are marked in the Chandra image in white (shock) and yellow.

Figure 11. A2218. The same as for Fig.3. The goodness of fits is reported in Fig.C9. The positions of the edges are marked in the Chandra image in white (shocks) and yellow.

Shocks and cold fronts in galaxy clusters

5609

possibly a cold front (however the temperature jump is not clearly detected, i.e.R = 0.84+0.35_−0.17), while the ‘outer’ one is consistent with a shock (R = 1.44+0.48_−0.33) and might be connected with the SE edge of the radio halo. The shock Mach numbers derived from SB and temperature jump areMSB= 1.17+0.10_−0.09andMkT = 1.45+0.43_−0.33, respectively. The SB profile taken in the SW region shows the hint of a kink (Fig.11j); in this case the broken power-law model (χ2_{/d.o.f.= 7.0/15) yields to an improvement compared to a}

sin-gle power-law fit (χ2_{/d.o.f.= 15.0/17), which according to the} F-test corresponds to a null-hypothesis probability of 3× 10−3

(3.0σ level). Spectral analysis leaves the nature of this feature uncertain.

5.1.10 Triangulum Australis

It is the closest (z= 0.051) cluster of our sample. Despite its prox-imity, it has been overlooked in the literature due to its low Galactic latitude. Markevitch, Sarazin & Irwin (1996) performed the most detailed X-ray analysis to date on this object using the Advanced

Satellite for Cosmology and Astrophysics (ASCA) and ROSAT and

revealed an overall hot temperature (∼10 keV) in its elongated ICM (Fig.12a). Neither XMM–Newton nor Chandra dedicated studies have been published on this system. Its K0value is reported

nei-ther in Cavagnolo et al. (2009) nor in Giacintucci et al. (2017), nonetheless its core was excluded to have low entropy by Rossetti & Molendi (2010). Recently, a diffuse radio emission classified as a halo has been detected (Scaife et al.2015; Bernardi et al.2016).

Three observations of Triangulum Australis can be found in the

Chandra data archive. However, the oldest two (ObsIDs 1227 and

1281) are calibration observations from the commissioning phase and took place less than 2 weeks after Chandra first light, when the calibration products had very large uncertainties. For this reason, we only used ObsID 17481 in our analysis.

From the maps of the ICM thermodynamical quantities in Figs12(d)–(f), one can infer the complex dynamical state of Trian-gulum Australis. The GGM filtered on the larger scale gives a hint of a straight structure in SB in the E direction, and it is described by our broken power law fit (C ∼ 1.3) in Fig.12(g). However, no temperature jump is detected across the edge, giving no clue about the origin of this SB feature. We mention that this region was also highlighted by Markevitch et al. (1996) with ASCA and ROSAT as a direct proof of recent or ongoing heating of the ICM in this cluster.

5.2 Summary of the detected edges

Overall, we found six shocks, eight cold fronts, and other eight discontinuities with uncertain origin due to the poorly constrained temperature jump. The properties of the detected edges are summa-rized in Table3, while the distributions ofC and R are displayed in Fig.13. Although we are not carrying out a statistical analysis of shocks and cold fronts in galaxy clusters, we notice that the majority of the reported jumps are associated with weak discontinuities with

C < 1.7 and 0.5 < R < 1.5. This may indicate that the GGMfilters

allow to pick up also small SB jumps that are usually lost in a visual inspection of unsmoothed cluster images.

We mention that in the case of a shock the SB and temperature jumps allow to give two independent constraints on the Mach num-ber (equation 9 and 10). However, so far, only few shocks reported in the literature have Mach number consistently derived from both

the jumps (e.g. A520, Markevitch et al.2005; A665, Dasadia et al.

2016; and A115, Botteon et al. 2016a). Instead, in our analysis there is a general agreement between these two quantities, further supporting the robustness of the results.

One could argue that the nature of the weakest discontinuities claimed is constrained at slightly more than 1σ level from the temperature ratio. This is a consequence of the small tempera-ture jump implied by these fronts and the large errors associated with the spectral analysis (despite the careful background treat-ment performed). However, we can check the presence of pressure discontinuities at these edges by combining the density and tem-perature jumps achieved from SB and spectral analysis. The values of P ≡ Pd/Pu= C × R computed for all the discontinuities are

reported in Table3and show at higher confidence levels the pres-ence of a pressure discontinuity in the shocks and the abspres-ence of a pressure jump in the cold fronts, strengthening our claims. Al-though this procedure combines a deprojected density jump with a temperature evaluated along the line of sight, we verified that given the uncertainties on the temperature determination and the errors introduced by a deprojection analysis, the projected and deprojected values of temperature and pressure ratios are statistically consistent even in the cases of the innermost edges (i.e. those more affected by projection effects).

With the present work, we increased the number of known shocks and cold fronts in galaxy clusters. The detected shocks have all

M < 2 likely due to the combination of the fact that shocks crossing

the central Mpc regions of galaxy clusters are weak (e.g. Vazza et al.

2012, and references therein) and that fast moving shocks would be present for a short time in the ICM.

The distinction between shock and cold fronts for the eight dis-continuities with uncertain origin can tentatively be inferred from the current values ofR and P reported in Table3. In this respect, deeper observations of these edges will definitely shed light about their nature.

5.3 Non-detections

Our analysis did not allow us to detect any edge in the following objects: A2813 (z= 0.292), A1413 (z = 0.143), A1689 (z = 0.183), and A3827 (z= 0.098). All these systems seem to have a more regular X-ray morphology (Figs14–17) with respect to the other clusters of the sample.

5.3.1 A2813

This cluster has a roundish ICM morphology (Fig.14a), nonetheless its value of K0= 268 ± 44 keV cm2is among the highest in our

sample (cf. Table 1). The core is slightly elongated in the NE– SW direction and has a temperature ∼7.7 keV, consistently with the XMM–Newton value reported by Finoguenov et al. (2005). The maps shown in Fig.14were produced using all the ObsIDs listed in Table2. We mention that the original target of the ACIS-S data sets (ObsIDs 16366, 16491, and 16513) is XMMU J0044.0−2033; however, A2813 is found to entirely lay on an ACIS-I chip that was kept on during the observations. These data provide the largest amount (∼80 per cent) of the total exposure time on A2813 and were used in our analysis although the unavoidable degradation of the instrument spatial resolution due to the ACIS-I chip being off-axis with this observing configuration.

Figure 12. Triangulum Australis. The same as for Fig.3. The goodness of fits is reported in Fig.C10. The position of the edge is marked in the Chandra image in yellow. Note that in the GGM filtered images the straight and perpendicular features are artefacts due to chip gaps.

Shocks and cold fronts in galaxy clusters

5611

Table 3. Properties of the jumps detected. Upper and lower bound errors onR and P were computed adding separately the negative error bounds and the positive error bounds in quadrature. Mach numbers from SB and temperature jumps are reported for shocks (S), for discontinuities whose nature is still uncertain (U), only the Mach derived from the SB is displayed, while for spectroscopically confirmed cold fronts (CF) the Mach number determination is not applicable (n.a.).

Cluster name Position C R P MSB MkT Nature

E 1.48+0.11_−0.10 – – 1.33+0.08_−0.07 – U

A370



W 1.56+0.13_−0.12 – – 1.38+0.10_−0.09 – U

SE inner 1.72+0.13_−0.12 0.74+0.14_−0.12 1.27+0.26_−0.22 n.a. n.a. CF

A399 

SE outer 1.45+0.10_−0.10 1.20+0.39_−0.26 1.74+0.58_−0.40 1.31+0.07_−0.07 – U

A401 SE 1.39+0.04_−0.04 0.78+0.07_−0.06 1.08+0.10_−0.09 n.a. n.a. CF

NW 2.50+0.29_−0.25 <0.59 <1.64 n.a. n.a. CF

MACS J0417.5−1154



SE 2.44+0.31_−0.25 0.44+0.17_−0.10 1.07+0.44_−0.27 n.a. n.a. CF

RXC J0528.9−3927 E 1.51+0.10_−0.09 0.73+0.25_−0.14 1.10+0.38_−0.22 n.a. n.a. CF

E inner 2.49+0.32_−0.26 0.62+0.33_−0.18 1.54+0.85_−0.48 n.a. n.a. CF MACS J0553.4−3342 ⎧ ⎨ ⎩ E outer 1.82+0.35−0.29 2.00+1.14−0.63 3.64+2.19−1.28 1.58+0.30−0.22 1.94+0.77−0.56 S W 1.70+0.12_−0.11 0.33+0.22_−0.12 0.56+0.38_−0.21 n.a. n.a. CF AS592 SW 1.99+0.17_−0.15 1.61+0.66_−0.43 3.20+1.34_−0.89 1.72+0.15_−0.12 1.61+0.54_−0.42 S

E upper 1.48+0.11_−0.12 0.40+0.21_−0.12 0.59+0.31_−0.18 n.a. n.a. CF A1914 ⎧ ⎨ ⎩ E lower 1.64+0.13−0.12 0.66+0.35−0.20 W 1.33+0.08_−0.07 1.27+0.26_−0.21 1.69+0.36_−0.29 1.22+0.06_−0.05 1.28+0.26_−0.21 S SE inner <1.47 1.33+0.27_−0.19 <2.36 <1.32 1.34+0.26_−0.20 S A2104 ⎧ ⎨ ⎩ SE outer 1.54+0.16−0.14 0.77+0.30−0.21 1.19+0.48−0.34 1.37+0.12−0.10 – U SW 1.27+0.07_−0.06 0.85+0.20_−0.15 1.08+0.26_−0.20 1.18+0.05_−0.04 – U N 1.47+0.21_−0.18 1.38+0.40_−0.28 2.03+0.66_−0.48 1.32+0.15_−0.13 1.39+0.37_−0.29 S SE inner 1.38+0.14_−0.11 0.84+0.35_−0.17 1.16+0.50_−0.25 1.26+0.10_−0.08 – U A2218 ⎧ ⎨ ⎩ SE outer 1.26+0.14−0.14 1.44+0.48−0.33 1.81+0.64−0.46 1.17+0.10−0.09 1.45+0.43−0.33 S SW 1.41+0.23_−0.21 1.41+0.83_−0.49 1.99+1.21_−0.75 1.28+0.17_−0.14 – U Triangulum Australis E 1.34+0.04_−0.04 1.00+0.15_−0.10 1.34+0.20_−0.14 1.23+0.03_−0.03 – U

Figure 13. Distribution of the central values ofC (top) and R (bottom) reported in Table3.

5.3.2 A1413

It has a border line value of K0(cf. Table1) from the threshold set

in this work. The distribution of cluster gas is somewhat elliptical, elongated in the N–S direction (Fig.15a). Our analysis and previ-ous Chandra temperature profiles (Vikhlinin et al.2005; Baldi et al.

2007) are in contrast with XMM–Newton that does not provide evi-dence of a CC (Pratt & Arnaud2002). This discrepancy is probably due to the poorer PSF of the latter instrument. A radio minihalo covering the CC region is also found by Govoni et al. (2009). The region in the NW direction with a possible discontinuity suggested by the GGM filtered images did not show the evidence for an edge with the SB profile fitting (Fig.D4).

5.3.3 A1689

It represents a massive galaxy cluster deeply studied in the optical band because its weak and strong gravitational lensing (e.g. Broad-hurst et al.2005; Limousin et al. 2007). The X-ray emission is quasi-spherical and centrally peaked (Fig.16a), features that appar-ently indicate a CC. Nevertheless, optical (Girardi et al.1997) and

XMM–Newton observations (Andersson & Madejski 2004) both suggest that the system is undergoing to a head-on merger seen along the line of sight due either to the presence of optical substruc-tures or to the asymmetric temperature of the ICM, hotter in the N. Our results confirm the presence of asymmetry in temperature distribution (Fig.16d). The fact that a radio halo is also detected (Vacca et al.2011) fits with the dynamically unrelaxed nature of the system.

Figure 14. A2813. The same as for Fig.3. The goodness of fits is reported in Fig.C11.

5.3.4 A3827

It constitutes another cluster studied in detail mainly for its opti-cal properties. Its central galaxy is one of the most massive known found in a cluster centre and exhibits strong lensing features (Car-rasco et al.2010). Gravitational lensing also indicates a separation between the stars and the centre of mass of the dark matter in the central galaxies (Massey et al.2015), making A3827 a good can-didate to investigate the dark matter self-interactions (Kahlhoefer et al.2015). On the X-ray side, the cluster emission is roughly spher-ical (Fig.17a), with an irregular temperature distribution (Fig.17d) and a mean value of ∼7 keV (Leccardi & Molendi 2008). Two regions to the E and W directions suggested by the GGM im-ages did not show any discontinuity with the SB profile fitting (Fig.D5).

6 C O N C L U S I O N S

Shocks and cold fronts produced in a collision between galaxy clusters give information on the dynamics of the merger and can be used to probe the microphysics of the ICM. Nonetheless their detection is challenged by the low number of X-ray counts in cluster outskirts and by possible projection effects that can hide these sharp edges. For this reason only a few of them have been successfully detected both in SB and in temperature jumps.

In this work we explored a combination of different analysis ap-proaches of X-ray observations to firmly detect and characterize edges in NCC massive galaxy clusters. Starting from GGM filtered images on different scales and the maps of the ICM thermodynam-ical quantities of the cluster, one can pinpoint ICM regions display-ing significant SB and/or temperature variations. These can be thus